---
title: "Short note: methods of calculating depreciation"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:short-note-depreciation-methods"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/short-note-depreciation-methods
site: BCT Engineering
---

# Short note: methods of calculating depreciation

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2067 Mangsir, 4 marks; 2066 Magh, 4 marks (asked 2 times)
- Video: [Engineering Economy - Depreciation Basic Concept and Calculator Technique (TAGLISH)](https://www.youtube.com/watch?v=cnnCX9OlCx0) — Engr. Beej
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/short-note-depreciation-methods
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

Write a short note on methods of calculating depreciation.

## Short answer

Depreciation allocates an asset's cost over its useful life. Straight-line gives equal yearly charges; declining-balance and sum-of-years'-digits accelerate deductions; sinking-fund builds a replacement fund; unit-of-production bases on usage; MACRS is for tax purposes. Accelerated methods increase early tax savings by providing larger upfront deductions.

## Answer

Depreciation is the decrease in the value of a physical asset with time and use. In accounting it is the systematic allocation of the cost of an asset (less salvage value) over its useful life. Common methods:

#### 1. Straight-line (SL) method
Equal charge each year: D = (P − S) / N, where P = cost, S = salvage value, N = life. Book value falls linearly. It is the simplest method.

#### 2. Declining-balance (DB) method
A fixed percentage of the opening book value is charged each year: D_k = R × BV_{k−1}. The charge is large in early years. The *double declining balance* (DDB) method uses R = 2/N. A fixed rate that brings book value exactly to S is R = 1 − (S/P)^(1/N).

#### 3. Sum-of-the-years'-digits (SOYD) method
D_k = (P − S) × (N − k + 1) / [N(N + 1)/2]. It is also an accelerated method: the fraction is largest in year 1.

#### 4. Sinking-fund method
A fund that grows at interest rate i is assumed to replace the asset. The yearly deposit is (P − S)(A/F, i, N) and depreciation in year k is the deposit × (F/P, i, k − 1). The charge is small early and larger later.

#### 5. Unit-of-production (service output) method
D = (P − S) × (units produced in the year / total expected units). It is suitable for machinery whose wear depends on use.

#### 6. MACRS (tax depreciation)
Property is placed in a class (3, 5, 7, 10 … year) and a fixed percentage table is used; it ignores salvage value.

Accelerated methods (DB, SOYD, MACRS) give larger deductions early, which reduce early taxes and raise present worth of after-tax cash flows.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the straight-line depreciation formula?
   A. D = (P - S)/N
   B. D = P/N
   C. D = (P - S)/(N - 1)
   D. D = R x opening book value
   Answer: A. Equal yearly charge of cost less salvage over life. (Key point: Straight line)

2. What rate does the double declining balance method use?
   A. R = 1/N of cost
   B. R = 2/N of opening book value
   C. R = 2/(N+1) of cost
   D. R = (P - S)/N
   Answer: B. DDB charges twice the straight-line rate on the declining book value. (Key point: Double declining balance)

3. How does the sinking-fund method distribute depreciation?
   A. Large early, small later
   B. Equal each year
   C. Small in early years, larger later
   D. Proportional to output
   Answer: C. Depreciation in year k = deposit x (F/P,i,k-1), which grows with k. (Key point: Sinking-fund pattern)

4. Why do accelerated methods (DB, SOYD, MACRS) benefit a firm?
   A. They increase total depreciation over the life
   B. They raise the salvage value
   C. They remove tax altogether
   D. Larger early deductions reduce early taxes and raise PW of after-tax cash flows
   Answer: D. Total depreciation is the same but taxes are deferred, which increases present worth. (Key point: Accelerated methods)

## Related in Engineering Economics

- [Define depreciation; list methods](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adepreciation-define-methods-list) — Engineering Economics, chapter 7